Instance-based sentence boundary determination by optimization

ABSTRACT

A method for instance-based sentence boundary determination optimizes a set of criteria based on examples in a corpus, and provides a general domain-independent framework for the task by balancing a comprehensive set of sentence complexity and quality constraints. The characteristics and style of naturally occurring sentences are simulated through the use of semantic grouping and sentence length distribution. The method is parameterized so that it is easily adapts to suit a Natural Language Generation (NLG) system&#39;s generation.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention generally relates to an instance-based sentenceboundary determination method and, more particularly, to a method forthe generation of sentences which are optimized by a set of criteriabased on examples in a corpus.

2. Background Description

The problem of sentence boundary determination in natural languagegeneration exists when more than one sentence is needed to conveymultiple concepts and relations. In the classic natural languagegeneration (NLG) architecture, sentence boundary decisions are madeduring the sentence planning stage in which the syntactic structure andwording of sentences are decided. Sentence boundary determination is acomplex process that directly impacts a sentence's readability, itssemantic cohesion, its syntactic and lexical realizability, and itssmoothness between sentence transitions. Sentences that are too complexare hard to understand, so are sentences lacking semantic cohesion andcross-sentence coherence. Furthermore, bad sentence boundary decisionsmay even make sentences unreadable.

Existing approaches to sentence boundary determination typically employone of the following strategies. The first strategy uses domain-specificheuristics to decide which propositions can be combined. For example,Proteus produces game descriptions by employing domain specific sentencescope heuristics. This approach can work well for a particularapplication; however, it is not readily reusable for new applications.The second strategy is to employ syntactic, lexical, and sentencecomplexity constraints to control the aggregation of multiplepropositions. These strategies can generate fluent complex sentences,but they do not take other criteria into consideration, such as semanticcohesion. Furthermore, since these approaches do not employ globaloptimization, the content of each sentence might not be distributedevenly. This may cause a dangling sentence problem, for example.

SUMMARY OF THE INVENTION

It is therefore an exemplary embodiment of the present invention toprovide a general and flexible sentence boundary determination frameworkwhich takes a comprehensive set of sentence complexity and qualityrelated criteria and automatically generates sentences that optimizethese criteria.

A further exemplary embodiment of the invention takes into considerationand is sensitive to not only the complexity of the generated sentences,but also their semantic cohesion, multi-sentence coherence and syntacticand lexical realizability.

It is another exemplary embodiment of the present invention to provide acomputer-implemented method that employs an instance-based method thatis sensitive to the style of the sentences in the application domain inwhich the corpus is collected.

It is still another exemplary embodiment of the present invention toprovide a computer-implemented method that can be adjusted easily tosuit a sentence generation system's capability and avoid some of itsknown weaknesses.

According to the invention, there is provided a sentence boundarydetermination framework that is executable within a multimodalconversation application. An example of a particular multimodalconversation application is in the real-estate domain in which potentialhome buyers interact with the system using multiple modalities, such asspeech and gesture, to request residential real-estate information.After interpreting the request, the system formulates a multimediapresentation, including automatically generated speech and graphics, asthe response. The sentence boundary determination method executingwithin the application takes a set of propositions selected by a contentplanner and passes the sentence boundary decisions to an instance-basedsentence generator, to formulate the final sentences.

BRIEF DESCRIPTION OF THE DRAWINGS

The foregoing and other objects, aspects and advantages will be betterunderstood from the following detailed description of a preferredembodiment of the invention with reference to the drawings, in which:

FIG. 1 is a system diagram which shows where the instance-based Sentenceboundary determination (ISBD) method would be implemented.

FIG. 2 is a flowchart that illustrates the optimization using examplecorpus and the overall cost function.

DETAILED DESCRIPTION OF A PREFERRED EMBODIMENT OF THE INVENTION

Referring now to FIG. 1, the instance-based sentence boundarydetermination by optimization method (ISBD) is implemented within thecapabilities of computing resources. The method is shown as a module 107within a domain 100. The domain can be any one of a multitude ofenvironments that accept requests for information and return theinformation in a sentence format. The domain example used throughoutthis description is that of the real-state domain. In the real estatedomain, a user can query a system for information regarding specifichouses, towns or schools. As the response to the user's query, thecontent selection application 104 returns the content, represented as aset of propositions, to be conveyed. The ISBD 107 would consult thedomain corpus 103 to optimize the content of each sentence to bereturned as the response to the query. Optimization is defined as asolution that is most similar to the examples in the corpus 103;consequently it can avoid dangling sentences, incoherent sentences,and/or semantic group splitting. Given the content of one or moresentences determined by ISBD 107, the sentence generation application106 would return a description of the requested houses, towns or schoolsin one or more grammatical sentences. The domain 100 is typicallyimplemented within a central processing unit. It interfaces withexternal data entry 101 and data output 102 elements through a network109. The network 109 may be any one of several types of connectivity toinclude but not be limited to a local area network, a wide area networksuch as, but not limited to, connectivity through the Internet.

The data entry 101 element may include but not be limited to a keyboard,a voice recognition device, mouse, a touch sensitive screen, or othersuch devices. The data output 102 element may include but not be limitedto computer screen, printer, video display, monitor, or other suchdevice. Likewise, the system for performing the method, software orfirmware containing the instruction set for performing the method can beprocessed within a central processing unit or other computer resource.The ISBD 107 optimizes the solution based on examples in a corpus 103which is stored either within the domain 100 or, as shown in FIG. 1, ina separate storage medium and/or database. The corpus 103 is accessedthrough a communication link 108. The communication link 108 may be alocal area or wide area network such as network 109. The communicationlink 108 may also be a direct connection such as a bus internal to thedomain 100. By accessing the corpus 103 to optimize the solution, theISBD 107 output sentences (or solution) can demonstrate properties, suchas comparable sentence length distribution and semantic grouping similarto those in the corpus. The ISBD 107 also avoids problematic sentenceboundaries by optimizing the solutions using all the instances in thecorpus.

The domain data 105 are accessed through communication link 108 and mayalso be stored either within the domain 100 or, as shown in FIG. 1, in aseparate storage medium and/or database. One example of the domain dataused in the real restate application is the MLS database that containsdescriptions of thousands of houses.

For the real estate domain example, a user would request details about aparticular house by entering request information through the data entry101 element. The content selection element 104 will decide all thecontent to be conveyed as the system's response to the request. Giventhose content, the ISBD 107 would examine the example sentences from thecorpus 103 and decide the number of sentences to be used in the responseand the content of each sentence. Given the content of each sentence,the sentence generation application 106 will produce one grammaticalsentence. In the end, one or more sentences are produced based on thesolutions of ISBD 107. Once the best sentence or set of sentences isproduced, the domain 100 would provide the solution to the user throughthe data output 102 element.

The variables that are used by the invention to calculate the variouscosts and weights for optimizing the solution relative to the particularquery from the user are shown in Table 1 TABLE 1 Instance-based SentenceBoundary Determination Variables P is the set of propositions to beconveyed SBC is the sentence boundary cost; there is an SBC wheneverthere is a sentence break C_(i) is a single instance/example within thecorpus P_(j) is a proposition in P_(,) C_(Hj) is the host sentence inthe corpus which contains the proposition p_(j,) icost is the insertioncost dcost is the deletion cost W_(i) is the insertion weight W_(d) isthe deletion weight N_(b) is the number of sentences in the solution Dcontains propositions in C_(i) that do not exist in P I containspropositions in P that are not in C_(i) O contains propositions in C_(i)that exist in P E_(j) any subset of I including Ø and I Q Containspropositions in I but not in Ej Cost (Q) is the cost of sbd(Q)

Referring now to the drawings, and more particularly to FIG. 2, there isshown the details of the sentence boundary determination algorithm,sbd(P), where P is the set of input propositions. Given an input, P, foreach corpus instance C_(i), a search branch is constructed representingall possible ways to realize the input using the instance plusdeletions, insertions and sentence breaks. Since each sentence breaktriggers a recursive call to the sentence boundary determinationalgorithm, the complexity of the algorithm is NP-hard. To speed up theprocess, in each iteration, unproductive branches are eliminated(pruned) using an upper bound derived by several greedy algorithms.

Step 201 sets the current upper bound, UB, to the minimum cost ofsolutions derived by any one of three greedy algorithms.

The first type of greedy algorithm that can be used to set the UB forinput P is a greedy set partition algorithm in which the corpus instanceC associated with the set {S|S ⊂P} with the largest |S| is selectedfirst. This process is repeated for each P′ where P′=P−S. The solutioncost is calculated using the relationship:Cost(P)=(N _(b)−1)*SBC,

Another type of greedy algorithm that will calculate the initial UB is agreedy minimum set covering algorithm. This algorithm can be employedwhen the corpus instance C associated with the set S that maximizes theoverlapping of propositions in P is found. The unwanted propositions inC are deleted. Assume P′=P−S, the delete process is performed for all P′until P′ is empty. The solution cost is again calculated using therelationship:Cost(P)=(N _(b)−1)*SBC+Σ _(i<b)Σ_(j)ε_(D)dcost(C _(i) ,P _(j)).

The only difference between this and the previous approach is that Shere might not be a subset of P.

A third type of greedy algorithm that will calculate the UB looks at amaximum overlapping sentence. First, this greedy algorithm identifiesthe instance C_(i) in the corpus that covers the maximum number ofpropositions in P. To arrive at a solution for P, the rest of thepropositions not covered by Ci are inserted into Ci and all the unwantedpropositions in Ci are deleted. The cost of this solution is:Wd*Σ _(pj)ε_(D)dcost(C _(i) ,p _(j))+W _(i)*Σ_(pk)ε_(i)icost(*,p _(k))in which D includes proposition in C_(i) but not in P, and I includespropositions in P but not in C_(i).

The invention starts with the initial UB calculation using the threegreedy algorithms and finds a sentence boundary solution that minimizesthe expected difference between the sentences resulting from theseboundary decisions and the examples in the corpus. The expecteddifferences are measured based on an overall cost function. They aredefined as: sentence boundary cost, insertion cost, and deletion cost.These costs are then evaluated through an expression to obtain the totalcost associated with the proposed solution. Although these costrelationships are used throughout the sentence boundary determinationmethod, they are defined here for clarity.

Sentence Boundary Cost (SBC):

Assuming P is a set of propositions to be conveyed and S is a collectionof example sentences selected from the corpus to convey P. Then P can berealized by S with a sentence boundary cost that is equal to (|S|−1)*SBCin which |S| is the number of sentences and SBC is the sentence boundarycost. To use a specific example from the real-estate domain, the input Phas three propositions:

p₁. House 1 has-attr (style=colonial).

p₂. House 1 has-attr(bedroom=3).

p₃. House 1 has-attr(bathroom=2).

One solution, S, contains 2 sentences:

s₁. This is a 3 bedroom, 2 bathroom house.

s₂. This is a colonial house.

Since only one sentence boundary is involved, S is a solution containingone boundary cost. In the above example, even though both s₁ and s₂ aregrammatical sentences, the transition from s₁ to s₂ is not quite smooth.They sound choppy and disjointed. To penalize this, whenever there is asentence break, there is a SBC. In general, the SBC is a parameter thatis sensitive to a generation system's capability such as its competencein reference expression generation. If a generation system does not havea robust approach for tracking the focus across sentences, it is likelyto be weak in referring expression generation and adding sentenceboundaries are likely to cause fluency problems. In contrast, if ageneration system is very capable in maintaining the coherence betweensentences, the proper sentence boundary cost would be lower.

Insertion Cost:

Assume P is the set of propositions to be conveyed, and C_(i) is aninstance in the corpus that can be used to realize P by inserting amissing proposition p_(j) to C_(i), then P can be realized using C_(i)with an insertion cost of icost(C_(H), p_(j)), in which C_(H) is thehost sentence in the corpus containing proposition p_(j). Using theexample from the real-estate domain, assume the input P=(p₂, p₃, p₄),where proposition

p₄. Housel has-attr (square footage=2000).

Assume C_(i) is a sentence selected from the corpus to realize P: “Thisis 3 bedroom 2 bathroom house”. Since C_(i) does not contain p₄, p₄needs to be added. P can be realized using C_(i) by inserting aproposition p₄ with an insertion cost of icost(C_(H), p₄), in whichC_(H) is a sentence in the corpus such as “This is a house with 2000square feet.”

The insertion cost is influenced by two main factors: the syntactic andlexical insertability of the proposition pj and a system's capability inaggregating propositions. For example, if in the corpus, the propositionp_(j) is always realized as an independent sentence and never as amodifier, icost(*, p_(j)) should be extremely high, which effectivelyprohibit pj from becoming a part of another sentence. icost(*, pj ) isdefined as the minimum insertion cost among all the icost(C_(H), p_(j)).Currently icost(C_(H), p_(j)) is computed dynamically based onproperties of corpus instances. In addition, since whether a propositionis insertable depends on how capable an aggregation module can combinepropositions correctly into a sentence, the insertion cost should beassigned high or low accordingly.

Deletion Cost:

Assume P is a set of input propositions to be conveyed and C_(i) is aninstance in the corpus that can be used to convey P by deleting anunneeded proposition p_(j) in C_(i). Then P can be realized using C_(i)with a deletion cost dcost(C_(i), p_(j)). As a specific example,assuming the input is P=(p₂,p₃, p₄), C_(i) is an instance in the corpus“This is a 3 bedroom, 2 bathroom, 2000 square foot colonial house.” Inaddition to the propositions p₂, p₃ and p₄, C_(i) also conveys aproposition p₁. Since p₁is not needed when conveying P, P can berealized using C_(i) by deleting proposition p₁ with a deletion cost ofdcost(C_(i), p₁). The deletion cost is affected by the syntacticrelation between p_(j) and its host sentence. Given a new instanceC_(i). “This 2000 square foot 3 bedroom, 2 bathroom house is acolonial”, deleting p₁, the main object of the verb, will make the restof the sentence incomplete. As a result, dcost(C_(i), p₁) is veryexpensive. In contrast, dcost(C_(i), p₄) is low because the resultingsentence is still grammatically sound. Currently dcost(C_(i), p_(j)) iscomputed dynamically based on properties of corpus instances. Anotherfactor affecting deletion cost is the expected performance of ageneration system. Depending on the sophistication of the generator tohandle various deletion situations, the expected deletion cost can behigh if the method employed is naive and error prone, or is low if thesystem can handle most cases accurately.

Overall Cost:

Assume P is the set of propositions to be conveyed and C is the set ofinstances in the corpus that are chosen to realize P by applying a setof insertion, deletion and sentence breaking operations, the overallcost of the solution:Cost(P)=Σ_(Ci)(W _(i)*Σ_(j)iCost(C _(Hj) ,p _(j))+W _(d)*Σ_(k)dcost(C_(i) ,p _(k)))+(N _(b)−1)*SBCin which W_(i), W_(d) and SBC are the insertion weight, deletion weightand sentence boundary cost; N_(b) is the number of sentences in thesolution, C_(i) is a corpus instance selected to construct the solutionand C_(Hj) is the host sentence that proposition p_(j) belongs.

Detailed Algorithm:

-   Step 201: set the initial upper bound UB to the lowest cost of    solutions derived by the greedy algorithms we described earlier.-   Loop A: For each instance C_(i) in corpus C in which at least one of    the propositions in P occurs [O=(C_(i)∩P)≠Ø], creating a search    branch. The goal here is to identify all the useful corpus sentence    examples for realizing P.-   Step 202, for each search branch constructed using C_(i), delete all    the propositions from C_(i) that are not part of the original P.    That is, deleting p_(j)εD in which D=C_(i)−P (D contains    propositions in C_(i) that do not exist in P).-   Step 203: computing the deletion operators and their associated    costs using the relationship:    Cost_(d)(P)=W _(d)*Σ_(pj)ε_(D)dcost(C _(i) ,p ₁)

Updating the overall cost.

-   In step 204, identifying all possible ways of adding propositions in    P but do not exist in C_(i). That is, let I=P−C_(i) (I contains    propositions in P but not in C_(i)).-   Loop B: for each subset E_(j) +532 I (E_(j) includes Ø and I    itself), generating a solution by:-   Step 205: inserting propositions in E_(j) into the existing instance    C_(i) and separating the rest and realizing them as independent    sentence(s).-   In step 206, updating the overall cost to:    Cost(P)=Cost_(d)(P)+W _(i)*Σ_(pk)ε_(Ej)icost(*,p_(k))-   In condition 1: check to see if the lower bound (LB) of the current    solution (or partial solution) is higher than established UB.-   If the answer is Yes, in step 207, prune the branch and stop the    search-   If the answer is No, in step 208, continue exploring the branch by    recursively compute SBD(Q) where Q=I−E_(j) and updating the overall    cost to:    Cost(P)=Cost(P)+SBC+Cost(Q)-   in which Cost(Q) is the cost of sbd(Q) which recursively computes    the best solution for input Q where Q⊂P.-   In step 209, update UB if Cost(P) is lower than established UB.-   Repeat the process until all the search branches are either visited    or pruned.-   In step 210, output the solution with the lowest overall cost.

In this preferred embodiment, UB is updated only after a completesolution is found. It is possible to derive better UB by establishingthe upper bound for each partial solution dynamically, but thecomputational overhead might not justify doing so.

While the invention has been described in terms of its preferredembodiment, those skilled in the art will recognize that the inventioncan be practiced with modification within the spirit and scope of theappended claims.

1. A computer-implemented optimization method for instance-basedsentence boundary determination comprising the steps of setting aninitial upper bound (UB) of a cost associated with an optimized solutionto a lowest cost derived by several greedy algorithms; identifying allcorpus instances stored in an electronic database that contains one ormore of a plurality of desired propositions; forming a search treestructure with branches for each of plurality of identified corpusinstances that contain one or more of said plurality of desiredpropositions; deleting one or more of a plurality of undesiredpropositions from said identified corpus instances; updating an overallcost with one or more deletion costs; inserting one or more of saidplurality of desired propositions that were not contained in said corpusinstance into said corpus instance; updating the overall cost with oneor more insertion costs; calculating a lower bound (LB) of a costassociated with a current solution or partial solution; pruning acurrent search branch if the LB is greater than the UB; recursivelycomputing a best solution associated with generating one or moreadditional sentences to convey the rest of said plurality of desiredpropositions that were not contained in said corpus instance; updatingthe overall cost with a boundary cost plus a cost associated with thebest solution found by the recursively computing procedure; updating UBif the current overall cost is lower than UB; and outputting a solutionthat has the lowest overall cost using a set of said identified corpusinstances with a set of said deletion, insertion and sentence breakoperations.
 2. The method of claim 1 wherein said step of setting theinitial UB is preformed using computing resources which considerinsertion costs, deletion costs, and sentence boundary costs, and setsan UB for the overall cost of the expected best solution using a greedyset partition algorithm.
 3. The method of claim 1 wherein said step ofsetting the initial UB is performed using computing resources whichconsider insertion costs, deletion costs, and sentence boundary costs,and sets an UB for the overall cost of the expected best solution usinga greedy minimum set covering algorithm.
 4. The method of claim 1wherein said step of setting the initial UB is performed using computingresources insertion costs, deletion costs, and sentence boundary costs,and sets an UB for the overall cost of the expected best solution usingone maximum overlapping sentence algorithm.
 5. The method of claim 1wherein said step of deleting one or more of a plurality of undesiredpropositions from said identified corpus is performed using a deletioncost of:Cost_(d)(C _(i) ,D)=W _(d)*Σ_(pj)ε_(D)dcost(C _(i) ,p _(j)) wherein, aset of variables of said set of relationship includes: D is a set ofpropositions to be deleted from C_(i), C_(i) is a single instance withinthe corpus, dcost is a deletion cost, W_(d) is a deletion weight, p_(j)is a proposition in D
 6. The method of claim 1 wherein said step ofinserting one or more of a plurality of desired propositions into saididentified corpus is performed using an insertion cost of:Cost_(i)(E)=W _(i)*Σ_(pj)ε_(E)icost(*,p _(j)) wherein, a set ofvariables of said set of relationship includes: C_(i) is the corpusinstance selected, E is a set of propositions to be inserted into C_(i),icost is an insertion cost, W_(i) is an insertion weight, p_(j) is aproposition in E, and
 7. The method of claim 1 wherein said step ofrecursively computing the best solution realizes the rest of one or moreof a plurality of desired propositions in separate sentences uses a costof:Cost_(s)(Q)=SBC+Cost(Q) wherein, a set of variables of said set ofrelationship includes: C_(i) is the corpus instance selected, Q is a setof propositions to be realized in different sentences, SBC is thesentence boundary cost, Cost(Q) is the cost associated with the bestsolution for realizing the set of propositions in Q
 8. The method ofclaim 1 further comprising the step of re-calculating said insertioncosts, said deletion costs and said sentence boundary costs with aoverall cost ofCost(P)=Cost_(d)(C _(i) ,D)+Cost_(i)(E)+SBC+Cost(Q) wherein, a set ofvariables of said set of relationship includes: P is a set ofpropositions to be conveyed, C_(i) is one of the instances within thecorpus identified to convey P, D is a set of propositions to be deletedfrom C_(i), I is a set of propositions to be added, E is a subset of Ito be inserted in C_(i), Q is the rest of propositions in I that will berealized in one or more different sentences (Q=I−E); SBC is a sentenceboundary cost of a natural language generator (NLG).
 9. A computerreadable medium having computer readable program code embodied thereinfor processing an optimization method for instance based sentenceboundary determination, the computer readable program code comprising:process for setting the initial upper bound (UB) of the cost associatedwith the optimized solution to the lowest cost derived by several greedyalgorithms; process for identifying all corpus instances stored inelectronic database that contain one or more of a plurality of desiredpropositions; forming a search tree structure with branches for each ofplurality of identified corpus instances that contain one or more ofsaid plurality of desired propositions; process for deleting one or moreof a plurality of undesired propositions from said identified corpusinstances; process for updating the overall cost with one or moredeletion cost; process for inserting one or more of said plurality ofdesired propositions that were not contained in said corpus instanceinto said corpus instance; process for updating the overall cost withone or more insertion cost; process for calculating the lower bound (LB)of the cost associated with the current solution (or partial solution);process for pruning the current search branch if the LB is greater thanthe established UB; process for recursively computing the best solutionassociated with generating one or more additional sentences to conveythe rest of said plurality of desired propositions that were notcontained in said corpus instance; updating the overall cost with aboundary cost plus the cost associated with the best solution found bythe recursive procedure; process for updating UB if the current overallcost is lower than UB; process for outputting a solution that has thelowest overall cost using a set of said identified corpus instances witha set of said deletion, insertion and sentence break operations.
 10. Thecomputer readable medium of claim 9 wherein said process for setting aninitial UP uses computing resources and considers insertion costs,deletion costs, and sentence boundary costs, and includes a process forsetting an upper bound for the overall cost of the expected bestsolution using a greedy set partition algorithm.
 11. The computerreadable medium of claim 9 wherein said process for setting an initialUP uses computing resources insertion costs, deletion costs, andsentence boundary costs, and includes a process for setting an upperbound for the overall cost of the expected best solution using a greedyminimum set covering algorithm.
 12. The computer readable medium ofclaim 9 wherein said process for setting uses computing resources andincludes insertion costs, deletion costs, and sentence boundary costs,and includes a process for setting an upper bound for the overall costof the expected best solution using a maximum one overlapping sentencealgorithm.
 13. The computer readable medium of claim 9 wherein saidprocess for deleting one or more of a plurality of undesiredpropositions from said identified corpus is performed using a deletioncost of:Cost_(d)(C _(i) ,D)=W _(d)*Σ_(pj)ε_(D)dcost(C _(i) ,p _(j)) wherein, aset of variables of said set of relationship includes: D is a set ofpropositions to be deleted from C_(i), C_(i) is a single instance withinthe corpus, dcost is a deletion cost, W_(d) is a deletion weight, p_(j)is a proposition in D
 14. The computer readable medium of claim 9wherein said process for inserting one or more of a plurality of desiredpropositions into said identified corpus is performed using an insertioncost of:Cost_(i)(E)=W _(i)*Σ_(pj)ε_(E)icost(*,p _(j)) wherein, a set ofvariables of said set of relationship includes: C_(i) is the corpusinstance selected, E is a set of propositions to be inserted into C_(i),icost is an insertion cost, W_(i) is an insertion weight, p_(j) is aproposition in E , and
 15. The computer readable medium of claim 9wherein said process for recursively computing realizes the rest of oneor more of a plurality of desired propositions in separate sentences anduses a cost of:Cost_(s)(Q)=SBC+Cost(Q) wherein, a set of variables of said set ofrelationship includes: C_(i) is the corpus instance selected, Q is a setof propositions to be realized in different sentences, SBC is thesentence boundary cost, Cost(Q) is the cost associated with the bestsolution for realizing the set of propositions in Q
 16. The computerreadable medium of claim 9 further comprising a process forre-calculating recalculates said insertion costs, said deletion costsand said sentence boundary costs with a overall cost ofCost(P)=Cost_(d)(C _(i) ,D)+Cost_(i)(E)+SBC+Cost(Q) wherein, a set ofvariables of said set of relationship includes: P is a set ofpropositions to be conveyed, C_(i) is one of the instances within thecorpus identified to convey P, D is a set of propositions to be deletedfrom C_(i), I is a set of propositions to be added, E is a subset of Ito be inserted in C_(i), Q is the rest of propositions in I that will berealized in one or more different sentences (Q=I−E); SBC is a sentenceboundary cost of a natural language generator (NLG).
 17. A computerizedsystem for optimization of instance-based sentence boundarydetermination comprising: data entry and data output devicesoperationally connected to a computerized domain; a corpus stored in anelectronic database and domain data accessible through a communicationslink and stored in a storage medium; said computerized domain performingthe following setting the initial upper bound (UB) of the costassociated with the optimized solution to the lowest cost derived byseveral greedy algorithms; identifying all corpus instances stored inelectronic database that contain one or more of a plurality of desiredpropositions; forming a search tree structure with branches for each ofplurality of identified corpus instances that contain one or more ofsaid plurality of desired propositions; deleting one or more of aplurality of undesired propositions from said identified corpusinstances; updating the overall cost with one or more deletion cost;inserting one or more of said plurality of desired propositions thatwere not contained in said corpus instance into said corpus instance;updating the overall cost with one or more insertion cost; calculatingthe lower bound (LB) of the cost associated with the current solution(or partial solution); pruning the current search branch if the LB isgreater than the established UB; recursively computing the best solutionassociated with generating one or more additional sentences to conveythe rest of said plurality of desired propositions that were notcontained in said corpus instance; updating the overall cost with aboundary cost plus the cost associated with the best solution found bythe recursive procedure; updating UB if the current overall cost islower than UB; outputting a solution that has the lowest overall costusing a set of said identified corpus instances with a set of saiddeletion, insertion and sentence break operations.